For the weekly schedules, see the Schedule.

Chapter 2 – Limits and derivatives

2.1   The tangent and velocity problems
2.2   The limit of a function
2.3   Calculating limits using the limit laws
2.4   The precise definition of a limit
2.5   Continuity
2.6   Limits at infinity; horizontal asymptotes
2.7   Derivatives and rates of change
2.8   The derivative as a function

Chapter 3 – Differentiation Rules

3.1   Derivatives of polynomials and exponential functions;
3.2   The Product and Quotient Rules
3.3   Derivatives of trigonometric functions
3.4   The Chain Rule
3.5   Implicit differentiation
3.6   Derivatives of logarithmic functions; see also 1.6
3.7   Rates of change in the natural and social sciences
3.8   Exponential growth and decay
3.9   Related rates
3.10 Linear approximations and differentials

Chapter 4 – Applications of Differentiation

4.1   Maximum and minimum values
4.2   The Mean Value Theorem
4.3   How derivatives affect the shape of a graph
4.4   Indeterminate forms and L’Hospital’s Rule
4.7   Optimization problems
4.8   Newton’s Method
4.9   Antiderivatives

Chapter 5 – Integrals (introduction)

5.1  Areas and distances
5.2  The definite integral and Riemann sums

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